Exact sampling of molecules in chemical space

TL;DR

This paper introduces a Monte Carlo-based method for directly sampling molecules in chemical space, enabling analysis of fundamental properties and relationships without exhaustive enumeration.

Contribution

It presents a novel Monte Carlo approach for exact sampling in chemical space, avoiding intractable enumeration and revealing inherent property trends.

Findings

Observed linear trends of property derivatives in chemical space.

Demonstrated the method's ability to sample without enumeration.

Revealed fundamental properties of chemical space.

Abstract

The concept of molecular similarity appears in many machine-learning algorithms based on the assumption that molecules with similar representations will also share similar properties. In this work, we propose a new way to study similarity measures in molecular graph space using a Monte Carlo approach. We enable direct sampling from the underlying distribution of chemical space without numerical approximations or complete enumeration of molecular graphs, the latter intractable for practically relevant graph sets of interest. The Monte Carlo method allows observation of several interesting fundamental properties of chemical space, such as a linear trend of average property derivatives in chemical space with respect to the property's value at the molecule of interest. The trend was observed for extensive and intensive properties, suggesting that this trend is an inherent property of chemical space.